Finite Group Databasebeta

← #11874986

Subgroups — #11874986

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594448C212yesmaximal
2#10592559C211yesmaximal, characteristic
3C3×#4858C211yesmaximal, characteristic, complemented
4C3×#4855C211yesmaximal, characteristic, complemented
5#10590889C211yesmaximal, characteristic, complemented
6#10590871C211yesmaximal, characteristic, complemented
7#10590712C211yesmaximal, characteristic
8C8×#624C211yesmaximal, characteristic
9#10590574C212yesmaximal
10#10590414C212yesmaximal, complemented
11#10590411C212yesmaximal, complemented
12#81916—31nomaximal
13#81891—31nomaximal
14C2×C8×C3⋊D3C2211yescharacteristic
15#64101C2212yes—
16C3×#890C2212yes—
17C3×#888C2212yes—
18#63918C2212yes—
19#63895—22no—
20#63888—22no—
21C4×#624C2211yescharacteristic
22#63869C2212yes—
23#63849C2212yes—
24#63843—22no—
25#63838—22no—
26C2×#3710C2211yescharacteristic
27C32×#106C2211yescharacteristic
28#63644C2211yescharacteristic
29#63634C2212yes—
30C3×#817C2211yescharacteristic
31C3×#817C2211yescharacteristic
32C3×C8×Dic3C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#807C2212yes—
36#63576C2212yes—
37#63575C2212yes—
38#63573C2212yes—
39Dic3×C3⋊C8C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5688—32no—
43C3×#499—31no—
44C3×#498—31no—
45#5078—32no—
46#5065—32no—
47#4880—32no—
48#4874—32no—
49#4860—31no—
50#4860—31no—
51#4860—31no—
52#4860—31no—
53#4860—32no—
54#4860—61no—
55#4858—32no—
56#4858—31no—
57#4858D311yescharacteristic, complemented
58#4855—31no—
59#4855D311yescharacteristic, complemented
60C4×D3×C8—31no—
61C4×D3×C8—31no—
62#4683—31no—
63#4680—31no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×C3×Dic6—22no—
66C2×#627—22no—
67C2×#624D412yes—
68C2×C32×C8C2311yescharacteristic
69C32×C4⋊C4C2312yes—
70#3752—22no—
71C4⋊(C3⋊Dic3)C2312yes—
72C4×C3⋊Dic3—22no—
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C8×C3⋊D3Q814yescomplemented
75C3×C4⋊Dic3—22no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—22no—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3C2311yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84#3724—22no—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88Dic32—22no—
89Dic32D412yes—
90#3710Q814yescomplemented
91#3160—91noSylow
92C3×C4⋊Q8—32no—
93C3×#125—32no—
94#946—62no—
95Q8×Dic3—62no—
96C2×D3×C8—31no—
97C2×D3×C8—31no—
98C2×D3×C8—31no—
99C2×D3×C8—31no—
100C2×D3×C8—61no—
101#897—62no—
102#896—62no—
103#896—62no—
104#892—32no—
105#892—32no—
106#892—32no—
107#892—32no—
108#892—62no—
109#890—32no—
110#890C2×D312yes—
111#888—32no—
112#888C2×D312yes—
113#887—62no—
114#887—62no—
115#887—62no—
116C42×D3—31no—
117C42×D3—31no—
118#870—32no—
119#869—32no—
120C3×#107—32no—
121C3×#106—21no—
122C3×#106—31no—
123C3×#106—31no—
124C3×#106—32no—
125C3×#106C2×D311yescharacteristic
126C3×#106C2×D311yescharacteristic
127C3×C4×C8—31no—
128C3×C4×C8—31no—
129#818—32no—
130#817—31no—
131#817—31no—
132#817—32no—
133#817—61no—
134#817C2×D311yescharacteristic
135#817C2×D311yescharacteristic
136C8×Dic3—31no—
137C8×Dic3—31no—
138C8×Dic3C2×D311yescharacteristic
139C8×Dic3C2×D311yescharacteristic
140#808—32no—
141#808C2×D312yes—
142#807—32no—
143#807—32no—
144#807—32no—
145#807—32no—
146#807—32no—
147#807—62no—
148#807C2×D312yes—
149C4×C3⋊C8—31no—
150C4×C3⋊C8—31no—
151C22×C3⋊D3C2×D411yescharacteristic
152C2×C32×C4—22no—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3C2×Q812yes—
157C4×C3⋊D3C2×Q812yes—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D412yes—
161C2×C3×Dic3C2×D412yes—
162C3×Dic6—44no—
163#627—44no—
164#624—24no—
165C32×C8C2×Q812yes—
166C3⋊(C3⋊C8)C2×Q812yes—
167C3×C3⋊C8C2×Q812yes—
168C3×C3⋊C8C2×Q812yes—
169#533—92no—
170#500—92no—
171#499—31no—
172#499—91no—
173#499—92no—
174#498—31no—
175#498—91no—
176#427—91no—
177#427—92no—
178#427—91no—
179C2×C4×C8—91no—
180C2×C3×Q8—62no—
181C2×C4×D3—31no—
182C2×C4×D3—31no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—61no—
186C2×Dic6—22no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C2×C3×C8—21no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8C22×D311yescharacteristic
193C2×C3×C8C22×D311yescharacteristic
194C3×C4⋊C4—22no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—62no—
198C3×C4⋊C4—62no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4C22×D312yes—
201C3×C4⋊C4C22×D312yes—
202C3×C42—31no—
203C3×C42—31no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—122no—
209C4⋊Dic3—22no—
210C4⋊Dic3—32no—
211C4⋊Dic3—32no—
212C4⋊Dic3—62no—
213C4⋊Dic3—62no—
214C4⋊Dic3—62no—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—22no—
218Dic3⋊C4—22no—
219Dic3⋊C4—62no—
220Dic3⋊C4—62no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C4×Dic3—122no—
230C4×Dic3C22×D311yescharacteristic
231C4×Dic3C22×D311yescharacteristic
232C2×C3⋊C8—31no—
233C2×C3⋊C8—31no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8C22×D311yescharacteristic
236C2×C3⋊C8C22×D311yescharacteristic
237D3×C8—34no—
238D3×C8—34no—
239D3×C8—34no—
240D3×C8—34no—
241D3×C8—64no—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3—22no—
244C2×C3⋊D3C4⋊Q812yes—
245C32×C4—42no—
246C32×C4C22×Q811yescharacteristic
247C32×C4C22×Q811yescharacteristic
248C3⋊Dic3—42no—
249C3⋊Dic3C4⋊Q812yes—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3#13514yes—
254C22×C8—91no—
255C22×C8—91no—
256C4⋊Q8—32no—
257C4⋊Q8—92no—
258#125—32no—
259#125—92no—
260C22⋊Q8—182no—
261C22⋊Q8—182no—
262C4×Q8—182no—
263C4×Q8—182no—
264#117—92no—
265#117—92no—
266C2×C42—91no—
267#107—32no—
268#107—92no—
269#107—92no—
270#107—92no—
271#106—31no—
272#106—31no—
273#106—32no—
274#106—92no—
275#106—91no—
276#106D3211yescharacteristic
277C4×C8—31no—
278C4×C8—31no—
279C4×C8—91no—
280C4×C8—91no—
281C22×D3—31no—
282C22×D3—31no—
283C22×D3—61no—
284C3×Q8—124no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—31no—
298C2×Dic3—31no—
299C2×Dic3—61no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3D3×D412yes—
304C2×Dic3D3×D412yes—
305C4×D3—32no—
306C4×D3—32no—
307C4×D3—32no—
308C4×D3—32no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—64no—
312C4×D3—64no—
313Dic6—44no—
314Dic6—124no—
315Dic6—124no—
316C3×C8—22no—
317C3×C8—32no—
318C3×C8—32no—
319C3×C8D3×Q812yes—
320C3×C8D3×Q812yes—
321C3⋊C8—32no—
322C3⋊C8—32no—
323C3⋊C8—62no—
324C3⋊C8D3×Q812yes—
325C3⋊C8D3×Q812yes—
326C2×C32C2×C4⋊Q811yescharacteristic
327C2×C32C2×#13512yes—
328C3⋊D3—22no—
329C2×Q8—62no—
330C2×Q8—182no—
331C22×C4—92no—
332C22×C4—91no—
333C2×C8—31no—
334C2×C8—31no—
335C2×C8—94no—
336C2×C8—91no—
337C2×C8—94no—
338C2×C8C2×D3211yescharacteristic
339C4⋊C4—32no—
340C4⋊C4—32no—
341C4⋊C4—62no—
342C4⋊C4—62no—
343C4⋊C4—62no—
344C4⋊C4—92no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4C2×D3212yes—
349C22⋊C4—182no—
350C22⋊C4—182no—
351C42—31no—
352C42—31no—
353C42—92no—
354C42—182no—
355C42—182no—
356C22×C3—21no—
357C22×C3C2×D3×D411yescharacteristic
358C22×C3C2×D3×D411yescharacteristic
359C2×D3—32no—
360C2×D3—32no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—122no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—34no—
368C3×C4—42no—
369C3×C4—42no—
370C3×C4—62no—
371C3×C4—82no—
372C3×C4—122no—
373C3×C4—122no—
374C3×C4C2×D3×Q811yescharacteristic
375C3×C4C2×D3×Q811yescharacteristic
376C3×C4C2×D3×Q811yescharacteristic
377C3×C4C2×D3×Q811yescharacteristic
378Dic3—22no—
379Dic3—32no—
380Dic3—32no—
381Dic3—42no—
382Dic3—42no—
383Dic3—62no—
384Dic3—122no—
385Dic3—122no—
386Dic3—242no—
387Dic3#91614yes—
388C32#316011yescharacteristic, complemented, Sylow
389C23—91no—
390Q8—124no—
391Q8—364no—
392C2×C4—22no—
393C2×C4—32no—
394C2×C4—32no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—91no—
398C2×C4—92no—
399C2×C4—92no—
400C2×C4—184no—
401C2×C4—182no—
402C2×C4C22×D3211yescharacteristic
403C8—32no—
404C8—32no—
405C8—92no—
406C8#379712yes—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3D3×C4⋊Q811yescharacteristic
410C2×C3D3×C4⋊Q811yescharacteristic
411C2×C3C2×#91612yes—
412C2×C3D3×#13512yes—
413D3—62no—
414D3—62no—
415D3—122no—
416C22—92no—
417C22—182no—
418C22D32×D411yescharacteristic
419C4—34no—
420C4—42no—
421C4—62no—
422C4—92no—
423C4—122no—
424C4—122no—
425C4—362no—
426C4C2×#379711yescharacteristic
427C4D32×Q811yescharacteristic
428C3—21no—
429C3#8189111yescharacteristic, complemented
430C3#8191611yescharacteristic, complemented
431C2—182no—
432C2#1059437411yescharacteristic
433C2D3×#91612yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#106D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C3×#4858C2semidirect
4. C3×#4855C2semidirect
5. #10590889C2semidirect
6. #10590871C2semidirect
10. #10590414C2semidirect
11. #10590411C2semidirect
57. #4858D3semidirect
59. #4855D3semidirect
74. C8×C3⋊D3Q8semidirect
90. #3710Q8semidirect
388. C32#3160semidirect
429. C3#81891semidirect
430. C3#81916semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105944482
#105925592
C3×#48582
C3×#48552
#105908892
#105908712
#105907122
C8×#6242
#105905742
#105904142
#105904112
#819163
#818913